Anaximenes, Pythagoras and Heraclitus: Air, Number, and the Puzzle of Change

Orientation #

He is continuing through the fragments of the first philosophers, having already treated Thales and Anaximander (prev. lecture), and now takes up Anaximenes, Pythagoras and Heraclitus. He breaks off with three Heraclitus fragments (DK 54, 51, 8) left for the students to think about and promises to talk about them next time.

The next class continues with Heraclitus.

The class, in order #

1. Anaximenes: air as beginning (“just as our soul, being air, holds us together”) #

Anaximenes, the third thinker, says air, not water or the unlimited, is the beginning of all things; the fragment shows he is moved by the importance of air for life.

• psuchē and English “spirit”/“ghost” go back to breath; calling God, angels, or the soul “spirit” carries a word for breath over to an immaterial substance — not the same meaning, but a likeness. Shakespeare: “these actors were all spirits, and are melted into air, into thin air.”
• Most people imagine the soul as an air-like substance in the shape of a man — Dante’s souls in purgatory, whom one tries to hug and cannot. But the soul is not air (On the Soul I).

2. Three reasons why air is a better guess than water (“that’s one of my stock questions on an exam”) #

Point: the sequence Mother Earth → water → air is a real advance, and he gives three reasons.

1. Quantitatively air is more unlimited than water (from Anaximander).
2. Qualitatively air is more unlimited — fewer qualities.
3. Third reason, reached only after the digression on the poets (below): air is thinner and finer in its parts.

• These reasons cannot show air better than the unlimited — nothing is more unlimited than the unlimited. Why then air rather than the unlimited? Presumably because he wanted something closer to the senses; “unlimited” is described only negatively. Air combines something still sensible with Anaximander’s insight.
• Digression on the poets, who precede the philosophers with Mother Earth: Shakespeare, Timon of Athens — “Common mother, thou whose womb immeasurable and infinite breast teems and feeds all” — earth as origin and as in a way infinite. “Mother” matters twice: materia comes from mater (a reason we do not call God our mother — it would suggest God is a cause in the sense of matter); and mother is the one who gives birth, and nature comes from birth (prenatal, nativity, “are you a native of Worcester?”; Shakespeare’s “revolts from true birth”). Aristotle first sees nature as matter, then as form, and shows nature is more form than matter. And “earth” is close to ground, the English word for cause — so cause, ground, nature and matter are all confused together in the poets.
• The order Mother Earth → water → air is from more known to us to less known to us, from more sensible to almost not sensible at all: empty the room of people and furniture and we all say “there’s nothing in there,” though there is air; the Sherlock Holmes chest opened and “empty.”
• Finer in parts: water comes through the basement wall where earth does not; air gets through where water does not.
• Thick from thin: his standard example — a thick book is made by putting together thin pages; you do not make a thin page out of thick books. Likewise molecules from atoms, atoms from elementary particles, particles from quarks — each thinner. So if you say “atom” and I say “elementary particle,” I have made the better guess.
• All three Milesians are from Miletus on the coast of Asia Minor (today Turkey).

3. Pythagoras: the octave and the turn to form (“the harmony of the octave comes in the ratio of two to one”) #

Pythagoras is an oddball, coming into natural philosophy from mathematics.

• The famous discovery: objects in the ratio 2:1 give the harmony of the octave — Greek diapason, dia “through” + pasōn “all,” you have gone through all and start over, do to do. He describes the demonstration with strings tuned alike and a wooden block moved halfway under one. Other harmonies also have simple numbers behind them.
• The Pythagoreans got carried away: maybe simple ratios lie behind everything. Hence the opinion Aristotle reports in On the Soul I that the soul is a self-moving number; hence numbers assigned to virtues — justice an even number, since justice asks “are we even now?” “I’ve got your number” is probably Pythagorean in origin.
• In mathematics you do not really have matter but you do have form; so a mathematician is inclined to look for that kind of cause. Form here is not only shape but ratio, order.
• Ratio examples: a Manhattan, two parts rye whiskey to one sweet vermouth; a Stinger, two parts brandy to one white crème de menthe — reverse it or make it half and half and it is cloying. Same matter, different ratio matters: carbon dioxide versus carbon monoxide — that ratio will kill you.

4. The word CAT: climbing from matter to the end (“what is worth saying can be said twice”) #

Point: the four causes are discovered in the order in which the mind notices dependences; the second cause is less well known than the first.

1. The most obvious, undeniable dependence of the word “cat” is on the letters C, A, T — take them away and nothing is left. That is like its matter.
2. But “act” has exactly the same letters and is not “cat.” So there is a second dependence, on order — form. Less obvious than the dependence on letters.
3. Do the letters explain how they get into that order? No — they do not rearrange themselves. So one is driven to the mover/maker, here the writer, with the ability to form and arrange letters.
4. But the writer’s ability extends to all orders — CAT, TAC (his daughter’s college, Thomas Aquinas College), ACT. So ability does not explain why this order: he wanted to speak of his favourite animal rather than of the college or of human acts. So one is forced to the final cause.

• The same ladder with the chair: the wood (take it and the screws out, nothing is left); another thing made of the same wood, so shape is a second cause; wood does not shape itself, so the carpenter; but he could have given it the shape of the chapel roof — “you are crazy, but I am able to do it” — so ability does not explain this shape, and we are forced back to the end.
• So these thinkers look first for matter, then see the need for form, then for the mover, and then with Socrates and Plato the end. “It’s beautiful how the human mind develops here.”
• Aside: Pythagoras started on Samos, then migrated to southern Italy, a centre of Pythagorean studies; Plato, fed up with Athens after Socrates’ death, went there and got the mathematical training that comes out in the Timaeus.

5. Heraclitus the central thinker (“the central thinker in human thought”) #

Heraclitus is at Ephesus, north of Miletus, some 500–600 years before St. Paul.

• He is central by analogy with the centre of a circle: from him Plato and Aristotle go one way, Hegel and Marx another, the physicists another, the evolutionists another.
• Plato was taught by Cratylus, a student of Heraclitus; there is a Platonic dialogue Cratylus, where Socrates seems put above him; yet Aristotle says in the Metaphysics that Plato even in old age was still quoting and following Cratylus. “Cratylus is a dimwit, but Heraclitus is a wit.”

6. “Nature loves to hide” (“I love that one”) #

Why does nature love to hide? Because nature is something within.

• Original meaning of nature is birth, and the baby comes from within, hidden (his daughter’s recent birth: they expected a boy, had thought about boys’ names, and “little old lady Sophia” came out). Then “nature” was carried over to the source of the baby within the mother — also hidden; then generalized to any cause of motion and rest within a thing; then to what a thing is — always something within. It is the outside of things that is known.
• Another reason: nature first means matter, and what is in matter; matter is a reason for hiding things, being not so actual. But the first reason is being within.
• Iago in Othello speaks of his inward nature, hidden at first; when he wears it on his sleeve, you will know what he is.
• He has seen a book in Borders titled Nature Loves to Hide, giving Heraclitus no credit.

7. The river and flux (“it is not possible to step twice into the same river”) #

Nature is defined by motion — the beginning and cause of motion and rest — and Heraclitus stresses the change in things with the image of the river, always flowing and never staying the same.

• Why can you not step twice into the same river? Because the river is water, and it is not the same water.
• Cratylus is supposed to have said you cannot step once into the same river: as your foot breaks the surface and goes down, the water has flowed on.
• We still say “the situation is fluid.”

8. The appearance of contradiction (“we step and do not step into the same rivers”) #

In the fragments DK 49–84 Heraclitus points out what seems to be a contradiction in changing things.

• Open question, left up in the air: did Heraclitus really think change involves something being and not being at once, or is he only producing that appearance?
• The test case put to the class: am I the same man who taught you last week? I have changed somewhat — lost some hair — and change is becoming other, so not the same. But it is the same man teaching, and the same students. So we are and we are not. “The sun is new every day.”
• Parmenides, reacting, rejects change as impossible because it involves contradiction; he is not in this collection because he is outside natural philosophy — no change, hence no nature.
• Plato and Aristotle take the other route: the contradiction is only apparent, so we do not yet understand change, and they set out to untie it. Hegel and Marx say there really is a contradiction; “as Comrade Lenin said, dialectics is the study of the contradictions in the essence of things.”

9. Change is between contraries (“cold things become warm”) #

A fragmentary form of the induction repeated by Socrates in the Phaedo and by Aristotle in Book I of Natural Hearing [ed.: Physics].

• Induction from many particulars: cold becomes warm and warm cold; the wet dries out and the dry is moistened; the hard is softened, the soft hardened; the healthy becomes sick and the sick healthy. Lukewarm seems a mixture of hot and cold, so everything goes back to the contraries.
• Socrates develops this in the first argument for the immortality of the soul.
• The puzzling application: “the same in us is the living and the dead, the waking and the sleeping, the young and the old; the former having changed are the latter, and these having changed are the former.”
• The argument from “become”: become means comes to be. If the cold comes to be hot, the cold is hot. If you do not mean that, why say it? And if the cold does not become hot, the cold will always be cold and there is no change. Likewise the ignorant could never become knowing.
• Hesiod is mocked for not knowing day and night, “for they are one” — he wrote Days and Nights as if they were two. If day becomes night, day is night.
• But another group of fragments shows Heraclitus does see a difference: for the waking there is one common world, and each sleeper turns aside into a world of his own. So he sees the difference yet says in words that they are the same.

10. The great dichotomy, and why Parmenides wins the point (“the most famous dichotomy in human thought”) #

The question: follow Heraclitus — everything changes, change involves contradiction, so something can both be and not be — or Parmenides — nothing can both be and not be, so change is an illusion?

• Parmenides: only a two-headed mortal could think it — you need one head to think it is so, another to think it is not; and a two-headed mortal is a monster, unnatural — yet Heraclitus says we should follow nature.
• The students’ first reply: our knowledge starts from the senses, and as Shakespeare says in Troilus and Cressida, “things in motion sooner catch the eye than what not stirs” — so change is real. A student answers Parmenides is more reasonable “if you’re just doing it analytically”; he agrees Parmenides seems more logical — you follow reason there, the other follows the senses.
• Heraclitus used against Heraclitus: he says we must follow what is common. If we disagree, it gets nowhere for each to say the other is wrong; we must get back to something we both agree about — as two scientists find an experiment that contradicts one prediction and not the other.
• What do Heraclitus and Parmenides have in common? At first sight nothing, since one affirms just what the other denies. But more deeply: both agree that you must choose between change and the impossibility of contradiction. And why must you choose? Because they apparently contradict each other — which is Parmenides’ own principle. So if Heraclitus is really choosing, he chooses on the basis of Parmenides’ principle. “So the ball game’s over. Parmenides is the one.”
• But it is absurd to deny that change exists, as Plato and Aristotle recognize. Hence the great discovery: since the principle is fundamental and change is undeniable, there must be a way of understanding change that does not involve a real contradiction, and under the apparent contradiction is hidden the way nature really is. That is the programme of Plato and Aristotle, and it is followed all the way to the Summa Theologiae. Aristotle treats this way of discovering things by untying contradictions at the beginning of Book III of Wisdom [ed.: Metaphysics], which they will read later.

11. “Changing it rests,” and paradox as a goad (“to make you stop and think”) #

Point: apparent contradictions dissolve when you see it is not the same thing that is at rest and in motion — and Heraclitus may state them so as to stimulate thinking.

• “I find travel very restful” — motion called restful: when the body is in motion the emotions calm down.
• The little boy told to sit still through a long church ceremony becomes restless: when his body is made to rest, his emotions get agitated. The reverse case.
• Bumper sticker: “the best things in life aren’t things.” On the surface self-contradictory. Solution by equivocal words: where something is said of two things and one keeps the common name while the other, adding something noteworthy, gets a new name — so “thing” is said of things and of persons, and persons get a new name. In one sense a person is a thing (not nothing); in another sense persons are divided against things. First “things” is in the common sense, the second is not.
• Same treatment again of “day becomes night.”
• DK 54, 51, 8 are left for the students; perhaps Heraclitus does not mean these things really are contradictory but wants to bring out the appearance, to make you stop and think.
• So does Thomas: at the head of each article three or four arguments against, then one on the other side — a little contradiction to make you think; the body of the article in earlier works is called the solutio, the untying. In the disputed questions there may be ten or fifteen on one side and five or ten on the other, so your mind really gets tied up, temporarily, and then you have to untie it.

His words #

• psuchē — the Greek for soul, from the word for breath.
• Unlimited — Anaximander’s principle, described only negatively [ed.: apeiron].
• Mother Earth — the poets’ first guess at the first matter; mater → materia, and mother → birth → nature.
• Ground — the English word for cause, close to “earth.”
• Thinner / finer in its parts — his mark of a better guess at first matter; thick book from thin pages.
• Diapason — dia “through” + pasōn “all”; the Greek name for the octave, ratio 2:1.
• Form — the second cause: not only shape but ratio and order.
• Self-moving number — the Pythagorean opinion about the soul.
• Two-headed mortal — Parmenides’ name for one who thinks it is and is not.
• Dialectical materialism — the official name of Marxist philosophy, its dialectical part from Hegel: real contradictions in things, the struggle of opposites giving rise to development.
• Natural Hearing [ed.: Aristotle’s Physics]; Wisdom, Book III [ed.: Metaphysics].
• Solutio — the body of the article in Thomas’s earlier works; in Latin, the untying.

Texts #

Read in class

• Handout of fragments of the first philosophers: Anaximenes on air and soul; Pythagoras on the octave in the ratio 2:1; Heraclitus — “nature loves to hide,” the river fragments, DK 49–84 (living/dead, waking/sleeping, young/old; the attack on Hesiod; “changing it rests”), the fragment on the one common world of the waking; DK 54, 51, 8 assigned for next time.
• Shakespeare, Timon of Athens: “Common mother, thou whose womb immeasurable and infinite breast teems and feeds all.”

Mentioned

• Shakespeare, The Tempest (inferred): “melted into air, into thin air”; Othello (Iago); Troilus and Cressida: “things in motion sooner catch the eye than what not stirs”; “revolts from true birth.”
• Dante (souls in purgatory).
• Aristotle, On the Soul I; Physics I; Metaphysics (Plato still quoting Cratylus); Metaphysics III.
• Plato, Phaedo; Cratylus; Timaeus.
• Hesiod, Days and Nights.
• Thomas Aquinas, Summa Theologiae; the disputed questions.

His questions #

• Why is air a better guess than water? (a stock exam question) — More unlimited quantitatively, more unlimited qualitatively, and thinner/finer in its parts.
• Why air rather than the unlimited? — Because he wanted something closer to the senses; “unlimited” is only a negative description.
• Is the first matter the thickest of things or the thinnest? — The thinnest: you make the thick out of the thin.
• Is justice an odd or an even number? — Even — justice asks “are we even now?”
• What is the most obvious dependence of the word “cat”? — On C, A and T, its matter; then on order, then on the writer, then on the end for which he wrote it.
• Why does nature love to hide? — Because nature is something within — birth from within, then the inner source, then what a thing is; only the outside is known.
• Why can you not step twice into the same river? — Because it is not the same water.
• Did Heraclitus really think change involves being and not being, or only its appearance? — Left open; his words admit it, but other fragments show he sees the difference.
• If you had to choose between Heraclitus and Parmenides, which is more reasonable? — Parmenides, since even choosing between the two rests on his principle.
• What do Heraclitus and Parmenides have in common? — Both assume one must choose between change and the impossibility of contradiction — and Plato and Aristotle deny just that assumption.